Cristina Odone is a journalist, novelist and broadcaster specialising in the relationship between society, families and faith. She is the director of communications for the Legatum institute and is a former editor of the Catholic Herald and deputy editor of the New Statesman. She is married and lives in west London with her husband, two stepsons and a daughter. Her new ebook No God Zone is now available on Kindle.

David Cameron might be juvenile, but he's no sexist

Very clever of Yvette Cooper, Labour leader-in-waiting, to portray herself as the woman who is tough on crime and tough on chauvinists. Super Cooper achieved the former with a speech at conference that sounded, in its small-c conservative support of the coppers, like David Blunkett. The latter she kept for a swipe at the Prime Minister which she delivered yesterday. Cameron's chauvinism was turning off women in droves, she told the conference: the Coalition was having "negative effects" on women, with cuts falling disproportionally on them.

Cooper reminded her supporters that Cameron proved he couldn't take women politicians seriously: he issued a patronising "calm down, dear" (listen to it, and judge) to Angela Eagle, the Labour MP in the Commons.

Clever tactics – but how true is Cooper's claim? Yes, Cameron's puerile, public-school sense of humour is lamentably geared to silly jokes: remember his dig at Nadine Dorries, regarding her feeling "frustrated"? It was almost Berlusconi-like in its boorishness. But at least the PM has a sense of humour. Anyone who comes in contact with the po-faced Labour Shadows is struck by how dull this lot is.

In any case, especially in politics, words don't count. Let's judge the PM by his actions – in public and in private.

Public-sector redundancies always affect women more than men, given the high proportion of public-sector women employees. Could Britain afford to keep a bloated state sector? No: cuts keep the country (women as well as men) from sliding into the economic abyss.

Flexi-hours at work and improved maternity and paternity leave: Cameron delivered both, despite a lot of resistance from business: that was aimed primarily at women.

Theresa May: when Gordon Brown appointed the disastrous Jacqui Smith as Home Secretary, Labour claimed that this was proof of how women-friendly their government was. (The fact that Smith paid for her husband's porn habit with taxpayers' money, you might think, mitigates against her uber-feminist image.) But Cameron has out-Browned Brown in appointing May, a consummate politician, in the post. There's been no fetishism about her sex; just lots of hard work and a polished performance by May.

But it is when you step away from the public arena to the private one that Cameron's true view of women becomes loud and clear. This is a man who champions his wife (yes, he married her – rather than keep her humiliatingly dangling until she'd borne him two sons, as Ed Miliband did to Justine) and supports her high-flying career. Cameron is a family man who ferried Ivan, his late son, to and fro hospital appointments. He changed the little boy's nappies and is now seen making time for his surviving children – from carrying baby Florence in a sling to taking in the football with Arthur.